Dynamic activation for an atomic force microscope and method of use thereof

ABSTRACT

A scanning probe microscope method and apparatus that modifies imaging dynamics using an active drive technique to optimize the bandwidth of amplitude detection. The deflection is preferably measured by an optical detection system including a laser and a photodetector, which measures cantilever deflection by an optical beam bounce technique or another conventional technique. The detected deflection of the cantilever is subsequently demodulated to give a signal proportional to the amplitude of oscillation of the cantilever, which is thereafter used to drive the cantilever.

CROSS-REFERENCE TO A RELATED APPLICATION

[0001] The present application is a continuation-in-part of U.S. patentapplication Ser. No. 09/476,163, filed on Dec. 30, 1999, which is acontinuation in-part of U.S. patent application No. 09/280,160, filed onMar. 29, 1999, each of these applications entitled ACTIVE PROBE FOR ANATOMIC FORCE MICROSCOPE AND METHOD OF USE THEREOF, the latter of whichis now issued as U.S. Pat. No. 6,189,374 B1 on Feb. 20, 2001.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to atomic force microscopes (AFMs)and, more particularly, to an AFM and method of use thereof thatdynamically controls the oscillating drive signal to the cantileverbased on the amplitude of the measured response of the cantilever.

[0004] 2. Description of the Related Art

[0005] An Atomic Force Microscope (“AFM”), as described in U.S. Pat. No.RE 34,489 to Hansma et al. (“Hansma”), is a type of scanning probemicroscope (“SPM”). AFMs are high-resolution surface measuringinstruments. Two general types of AFMs include contact mode (also knownas repulsive mode) AFMs, and cyclical mode AFMs (periodically referredto herein as TappingMode™ AFMs.)

[0006] The contact mode AFM is described in detail in Hansma. Generally,the contact mode AFM is characterized by a probe having a bendablecantilever and a tip. The AFM operates by placing the tip directly on asample surface and then scanning the surface laterally. When scanning,the cantilever bends in response to sample surface height variations,which are then monitored by an AFM deflection detection system to mapthe sample surface. The deflection detection system of such contact modeAFMs is typically an optical beam system, as described in Hansma.

[0007] Typically, the height of the fixed end of the cantilever relativeto the sample surface is adjusted with feedback signals that operate tomaintain a predetermined amount of cantilever bending during lateralscanning. This predetermined amount of cantilever bending has a desiredvalue, called the setpoint. Typically, a reference signal for producingthe setpoint amount of cantilever bending is applied to one input of afeedback loop. By applying the feedback signals generated by thefeedback loop to an actuator within the system, and therefore adjustingthe relative height between the cantilever and the sample, cantileverdeflection can be kept constant at the setpoint value. By plotting theadjustment amount (as obtained by monitoring the feedback signalsapplied to maintain cantilever bending at the setpoint value) versuslateral position of the cantilever tip, a map of the sample surface canbe created.

[0008] The second general category of AFMs, i.e., cyclical mode orTappingMode™ AFMs, utilize oscillation of a cantilever to, among otherthings, reduce the forces exerted on a sample during scanning. Incontrast to contact mode AFMs, the probe tip in cyclical mode makescontact with the sample surface or otherwise interacts with it onlyintermittently as the tip is scanned across the surface. Cyclical modeAFMs are described in U.S. Pat. Nos. 5,226,801, 5,412,980 and 5,415,027by Elings et al.

[0009] In U.S. Pat. No. 5,412,980, a cyclical mode AFM is disclosed inwhich a probe is oscillated at or near a resonant frequency of thecantilever. When imaging in cyclical mode, there is a desired tiposcillation amplitude associated with the particular cantilever used,similar to the desired amount of cantilever deflection in contact mode.This desired amplitude of cantilever oscillation is typically keptconstant at a desired setpoint value. In operation, this is accomplishedthrough the use of a feedback loop having a setpoint input for receivinga signal corresponding to the desired amplitude of oscillation. Thefeedback circuit servos the vertical position of either the cantilevermount or the sample by applying a feedback control signal to a Zactuator so as to cause the probe to follow the topography of the samplesurface.

[0010] Typically, the tip's oscillation amplitude is set to be greaterthan 20 nm peak-to-peak to maintain the energy in the cantilever arm ata much higher value than the energy that the cantilever loses in eachcycle by striking or otherwise interacting with the sample surface. Thisprovides the added benefit of preventing the probe tip from sticking tothe sample surface. Ultimately, to obtain sample height data, cyclicalmode AFMs monitor the Z actuator feedback control signal that isproduced to maintain the established setpoint. A detected change in theoscillation amplitude of the tip and a resulting feedback control signalare indicative of a particular surface topography characteristic. Byplotting these changes versus the lateral position of the cantilever, amap of the surface of the sample can be generated.

[0011] Notably, AFMs have become accepted as a useful metrology tool inmanufacturing environments in the integrated circuit and data storageindustries. A limiting factor to the more extensive use of the AFM isthe limited throughput per machine due to the slow imaging rates of AFMsrelative to competing technologies. Although it is often desirable touse an AFM to measure surface topography of a sample, the speed of theAFM is typically far too slow for production applications. For instance,in most cases, AFM technology requires numerous machines to keep pacewith typical production rates. As a result, using AFM technology forsurface measurement typically yields a system that has a high cost permeasurement. A number of factors are responsible for these drawbacksassociated with AFM technology, and they are discussed generally below.

[0012] AFM imaging, in essence, typically is a mechanical measurement ofthe surface topography of a sample such that the bandwidth limits of themeasurement are mechanical ones. An image is constructed from a rasterscan of the probe over the area to be imaged. In both contact andcyclical mode, the tip of the probe is caused to scan across the samplesurface at a velocity equal to the product of the scan size and the scanfrequency. As discussed previously, the height of the fixed end of thecantilever relative to the sample surface can be adjusted duringscanning at a rate typically much greater than the scanning rate inorder to maintain a constant force (contact mode) or oscillationamplitude (cyclical mode) relative to the sample surface.

[0013] Notably, the bandwidth requirement for a particular applicationof a selected cantilever is generally predetermined. Therefore, keepingin mind that the bandwidth of the height adjustment (hereinafterreferred to as the Z axis or Z-position bandwidth) is dependent upon thetip velocity as well as the sample topography, the required Z-positionbandwidth typically limits the maximum scan rate for a given sampletopography.

[0014] Further, the bandwidth of the AFM in these feedback systems isusually lower than the open loop bandwidth of any one component of thesystem. In particular, as the 3 dB roll-off frequency of any componentis approached, the phase of the response is retarded significantlybefore any loss in amplitude response. The frequency at which the totalphase lag of all the components in the system is large enough for theloop to be unstable is the ultimate bandwidth limit of the loop. Whendesigning an AFM, although the component of the loop which exhibits thelowest response bandwidth typically demands the focus of designimprovements, reducing the phase lag in any part of the loop willtypically increase the bandwidth of the AFM as a whole.

[0015] With particular reference to the contact mode AFM, the bandwidthof the cantilever deflection detection apparatus is limited by amechanical resonance of the cantilever due to the tip's interaction withthe sample. This bandwidth increases with the stiffness of thecantilever. Notably, this stiffness can be made high enough such thatthe mechanical resonance of the cantilever is not a limiting factor onthe bandwidth of the deflection detection apparatus, even thoughsensitivity to increased imaging forces may be compromised.

[0016] Nevertheless, in contact mode, the Z position actuator stilllimits the Z-position bandwidth. Notably, Z position actuators for AFMsare typically piezo-tube or piezo-stack actuators which are selected fortheir large dynamic range and high sensitivity. Such devices generallyhave a mechanical resonance far below that of the AFM cantilever broughtin contact with the sample, typically around 1 kHz, thus limiting theZ-position bandwidth.

[0017] Manalis et al. (Manalis, Minne, and Quate, “Atomic forcemicroscopy for high speed imaging using cantilevers with an integratedactuator and sensor,” Appl. Phys. Lett., 68 (6) 871-3 (1996))demonstrated that contact mode imaging can be accelerated byincorporating the Z position actuator into the cantilever beam. Apiezoelectric film such as ZnO was deposited on the tip-side of thecantilever. The film causes the cantilever to act as a bimorph such thatby applying a voltage dependent stress, the cantilever will bend. Thisbending of the cantilever, through an angle of one degree, or even less,results in microns of Z positioning range. Further, implementing the Zposition actuator in the cantilever increases the Z-position bandwidthof the contact mode AFM by more than an order of magnitude.

[0018] Nevertheless, such an AFM exhibits new problems with the Zpositioning which were not concerns with other known AFMs. For instance,the range of the Z actuator integrated with the cantilever is less thanis required for imaging many AFM samples. In addition, because thepositioning sensitivity of each cantilever is different, the AFMrequires recalibration whenever the probe is changed due to a worn orbroken tip. Further, the sensitivity in some cases exhibits undesirablenon-linearity at low frequencies. These problems can make the Z actuatorintegrated with the cantilever a less than optimal choice for generaluse as the Z actuator in commercial AFMs.

[0019] Furthermore, notwithstanding the above, in many AFM imagingapplications, the use of contact mode operation is unacceptable.Friction between the tip and the sample surface can damage imaged areasas well as degrade the tip's sharpness. Therefore, for many of theapplications contemplated by the present invention, the preferred modeof operation is cyclical mode, i.e., TappingMode. However, the bandwidthlimitations associated with cyclical mode detection are typically fargreater than those associated with contact mode operation.

[0020] In cyclical or non-continuous contact mode operation, the AFMcantilever is caused to act as a resonant beam in steady stateoscillation. When a force is applied to the cantilever, the force can bemeasured as a change in either the oscillation amplitude or frequency.One potential problem associated with cyclical mode operation is thatthe bandwidth of the response to this force is proportional to 1/Q(where Q is the “quality factor” of the natural resonance peak), whilethe force sensitivity of the measurement is proportional to the Q of thenatural resonance peak. Because, in many imaging applications, thebandwidth is the primary limiting factor of scan rate, the Q is designedto be low to allow for increased imaging speeds. However, reducing the Qof the cantilever correspondingly reduces force detection sensitivity,which thereby introduces noise into the AFM image.

[0021] A further contributing factor to less than optimal scan rates incyclical mode operation is the fact that the amplitude error signal hasa maximum magnitude. Over certain topographical features, a scanning AFMtip will pass over a dropping edge. When this occurs, the oscillationamplitude of the cantilever will increase to the free-air amplitude,which is not limited by tapping on the surface. The error signal of thecontrol loop is then the difference between the free-air amplitude andthe set point amplitude. In this instance, the error signal is at amaximum and will not increase with a further increase in the distance ofthe tip from the sample surface. The topography map will be distortedcorrespondingly.

[0022] Finally, the maximum gain of the control loop in cyclical mode islimited by phase shifts, thus further limiting the loop bandwidth. Inview of these drawbacks, the Z position measurement for an atomic forcemicroscope is typically characterized as being slew rate limited by theproduct of the maximum error signal and the maximum gain.

[0023] As a result, AFM technology posed a challenging problem if thescan rate in cyclical mode was to be increased significantly. Onegeneral solution proposed by Mertz et al. (Mertz, Marti, and Mlynek,“Regulation of a microcantilever response by force feedback,” Appl.Phys. Lett. 62 (19) at 2344-6 (1993)) (hereinafter “Mertz”), but notdirected to existing cyclical mode AFMs, included a method fordecreasing the effective Q of a cantilever while preserving thesensitivity of the natural resonance. In this method, a feedback loop isapplied to the cantilever resonance driver such that the amplitude ofthe driver to the cantilever is modified based on the measured responseof the cantilever. This technique serves to modify the effective Q ofthe resonating cantilever and will be referred to hereinafter as “activedamping.” Mertz accomplished active damping by thermally exciting thecantilever by first coating the cantilever with a metal layer that haddifferent thermal expansion properties than the cantilever beam itself.Then, in response to the feedback signals, Mertz modulated a laserincident on the cantilever, so as to apply a modified driving force.

[0024] When active damping is applied to the Mertz structure, mechanicalresonances other than that of the cantilever are excited, and the gainof the active damping feedback cannot be increased enough tosignificantly modify the effective cantilever Q. Further, the Mertzdesign is prohibitively inflexible for systems contemplated by thepresent invention due to the fact that, among other things, themodulating laser only deflects the cantilever in one direction. Thisintroduces a frequency doubling effect that must be accounted for toprocess the output. Overall, the Mertz system is complex and producesmarginally reliable measurements at undesirably slow speeds.

[0025] In previous embodiments of the invention, an AFM with a Zposition actuator and a self-actuated Z position cantilever (bothoperable in cyclical mode and contact mode), was implemented withappropriately nested feedback control circuitry to achieve high-speedimaging and accurate Z position measurements. The feedback signalsapplied to each of the actuators are independently monitored to indicatethe topography of the sample surface, depending upon the scan rate andsample topography. Further, the feedback system can modify the effectiveQ of a resonating cantilever without exciting mechanical resonance'sother than that of the cantilever. As a result, the system can optimizethe Z-position bandwidth of the cantilever response to maximizescanning/imaging speeds, yet preserve instrument sensitivity.

[0026] Notably, however, the AFM cantilever is typically a consumablepart of the system. The AFM cantilever tip wears out during the courseof normal usage and must be frequently replaced. Each time a new AFMcantilever is introduced to the system, the driving oscillator must beadjusted to the natural resonance of the cantilever. In the previousembodiments of the Q modifying circuit, the cantilever is driven notonly by the oscillator, but also by a filtered function of its owndeflection. For each new cantilever, the transfer function of the Qmodifying filter must be adjusted to optimize the response of thecantilever. This adjustment can be difficult to automate and typicallyrequires either extensive computer processing or the intervention of anexpert user.

SUMMARY OF THE INVENTION

[0027] The preferred embodiment of the present invention increases thespeed and ease of use of an AFM by including an amplitude detectioncircuit to dynamically control the cantilever drive signal in theamplitude domain. In particular, by demodulating the cantilever responsebefore it is used to modify the drive signal to the cantilever, the needto adjust the transfer function of a Q modifying filter in the feedbackpath is eliminated, thus making operation more cost-effective,efficient, and allowing ready substitution of different cantilevers.

[0028] Similar to previous embodiments, the present invention preferablycombines an AFM Z position actuator and a self-actuated Z positioncantilever (both operable in cyclical mode and contact mode), withappropriately nested feedback control circuitry to achieve high-speedimaging and accurate Z position measurements. The feedback signalsapplied to each of the actuators can be independently monitored toindicate the topography of the sample surface, depending upon the scanrate and sample topography.

[0029] According to another aspect, the lower frequency topographyfeatures of a sample, including the slope of the sample surface, arefollowed by a standard Z actuator while the high frequency components ofthe surface topography are followed by the self-actuated cantilever.Preferably, two feedback loops are employed. The first feedback loopcontrols the self-actuated cantilever to maintain a relatively constantforce between the tip of the cantilever and the sample surface. Thesecond feedback loop controls the standard Z actuator, at a lower speedthan the first feedback loop and serves either (1) to keep theself-actuated cantilever within its operating Z range or (2) to maintainthe linearity of the positioning sensitivity of the cantilever whenfollowing low frequency topography. This embodiment also allows for thestandard Z actuator to be exclusively used for accurate heightmeasurements when the scan rate is sufficiently lowered, typically lessthan 500 μm/sec.

[0030] According to a preferred embodiment, an AFM which operates incyclical mode (i.e., TappingMode™) combines both the AFM Z actuator andthe self-actuated cantilever with appropriate feedback control in asystem that oscillates the self-actuated actuator without introducingmechanical resonance's other than that of the cantilever. Most notably,in this preferred embodiment, the self-actuated cantilever is notoscillated by vibrating a piezo-crystal mechanically coupled to thecantilever, but rather is oscillated at its resonance by directlyexciting the piezoelectric material disposed thereon. This eliminatesmechanical resonance's in the coupling path which would otherwise bepresent.

[0031] As suggested above, the speed of a standard AFM in cyclical modeis generally limited by the loop bandwidth of the force detectioncircuitry and the Z positioning apparatus. A further limiting factorassociated with standard AFMs pertains to phase shift contributions fromthe various components of the loop that accumulate to limit the gain ofan otherwise stable operating system. Importantly, however, theself-actuated cantilever does not have significant phase shiftcontributions at standard operating frequencies, even though thedetection bandwidth of the AFM in cyclical mode is still limited by thewidth of the resonance peak of the cantilever. Therefore, theself-actuated cantilever feedback loop is considerably faster than theAFM Z position actuator feedback loop, when both are limited by the samedetection bandwidth. Notably, however, this embodiment also increasesthe speed of the AFM Z actuator feedback loop by providing a largererror signal than that which is generated by the cyclical mode amplitudedeflection detector.

[0032] Next, the combination of the standard AFM Z actuator and theself-actuated cantilever allows for greater flexibility in fast scanningcyclical mode. When the Z actuator feedback loop is disabled oroperating with low gain, the topography appears as the control signal tothe self-actuated cantilever. This control signal preferably also servesas the error signal for the second or AFM Z actuator feedback loop. Whenthe gain of the second feedback loop is optimized, i.e., when the Zactuator is operating as fast as possible without yielding unreliableoutput, the topography then appears in the control signal for the AFM Zposition actuator. As a result, by incorporating the self-actuatedcantilever within the control loop, the speed of obtaining highlyaccurate sample characteristic measurements can be increased. Also, asin previous embodiments, the standard Z actuator can be used to removeslope or non-linearities from the scan in the case in which theself-actuated cantilever follows the topography of the sample surface.Further, as an alternative to a standard Z actuator such as apiezo-stack actuator, a thermal actuator disposed on the self-actuatedcantilever can be used.

[0033] Another preferred embodiment uses the integrated piezoelectricelement of a self-actuated cantilever to modify the Q of the mechanicalresonance of the cantilever. In operation, the cantilever resonancepreferably is excited with the integrated piezoelectric element, ratherthan with a mechanically coupled driving piezo-crystal. The circuitwhich provides the cantilever drive signal modifies the Q of the leverwith feedback from the detected deflection signal.

[0034] In particular, according to one preferred embodiment, thedeflection signal is phase shifted, preferably by 90 degrees, and addedback to the cantilever drive signal. This feedback component of thedrive signal modifies the damping of the cantilever resonance (i.e.,active damping) and thereby controllably decreases or enhances the Q.Alternatively, the deflection signal can be fed to a differentiator tomodify the Q of the mechanical resonance of the cantilever. Thedifferentiated signal is added back to the cantilever drive signal as afeedback signal to provide the active damping. Notably, in thisalternative embodiment, the Q can be modified to provide activeenhancement, for example, to increase the sensitivity of the response.When modification of the cantilever Q is combined with the structure ofthe previously described embodiment wherein the self-actuated cantileveris used for Z positioning in synchronicity with an AFM Z positionactuator, the scan speed of the AFM in cyclical mode can be increased byan order of magnitude or more.

[0035] Moreover, in an effort to avoid the negative effects associatedwith positive feedback in the system (described below), a preferredembodiment of the present invention may include a bandpass filtercentered around the peak of desirable operation. The filter ispreferably disposed at the output of the cantilever drive circuit so asto insure that the system damps the peak, thus allowing the system toachieve damping up to a factor of, for example, a hundred, rather than amaximum factor of fifty with the above-described systems.

[0036] Further, although the system described immediately above achievessignificant damping by insuring that the peak is damped, because eachcantilever may have a different resonant frequency, the phase shifterincluded in the damping feedback circuit will have to be adjusted. It isdesirable to not have to account for differences in cantilevers thatwill be used with the system. All filters (for example, thejust-described bandpass filter) have a phase shift associated with them.Such a phase shift typically must be quantified and accounted for, andthat can be accomplished in the phase shifter for a particular frequencycantilever. However, making adjustments to the phase shifter each time acantilever is replaced is tedious and thus does not lend itself well tocurrent high throughput demands.

[0037] As a result, in another preferred embodiment of the invention,the imaging dynamics are modified by an active drive technique tooptimize the bandwidth of amplitude detection. The deflection ispreferably measured by an optical detection system including a laser anda photodetector, which measures cantilever deflection by an optical beambounce technique or another conventional technique. The detecteddeflection of the cantilever is subsequently demodulated to give asignal proportional to the amplitude of oscillation of the cantilever,which is used to drive the cantilever. Note that one advantage of thispreferred embodiment is that the self-actuated probe is not required forthe dynamic drive circuit to be effective. For example, if apiezo-crystal mechanically coupled to the cantilever is employed todrive the cantilever, any resonances introduced thereby will not affectthe active damping because the active damping circuitry is operating inthe amplitude domain and thus does not have to compensate for frequencyeffects. This is contrary to the previous active damping embodimentswhich operate in the frequency domain. As a result, the performance ofthe active damping of the AFM cantilever of the present embodiment isnot considerably reduced when the cantilever is not the self-actuatedtype.

[0038] Continuing, as described with respect to tapping mode imaging, adesired operating amplitude of the cantilever oscillation is representedby the amplitude setpoint. The amplitude setpoint is subtracted from thedemodulated amplitude signal to generate a deflection amplitude errorsignal. This amplitude error signal is then used to scale the drivesignal to the cantilever. In particular, this embodiment typicallydrives the cantilever with some nominal steady state amplitude and addsto that drive, a dynamic drive amplitude which is proportional to thedeflection amplitude error signal.

[0039] For increased speed, the drive amplitude is controlled withnegative feedback from the deflection amplitude error signal. When theprobe moves toward the sample surface, the response amplitude of theprobe will naturally decrease, giving a negative decreasing amplitudeerror signal. The dynamic drive feedback will then increase the drive tothe cantilever. While scanning, the probe tip may encounter an upwardgoing step, for example. The oscillation amplitude of the cantileverwill be limited by the sample surface to a lower RMS value. The Zposition feedback loop responds by moving the probe away from thesurface. This is the point at which more drive amplitude is requiredsuch that the cantilever tip will continue to tap on the surface. Sincethe RMS amplitude is reduced, the dynamic drive circuit will besupplying the cantilever with increased drive signal amplitude to meetthat need.

[0040] For gentler imaging, the drive amplitude is controlled withpositive feedback from the deflection amplitude error signal. When theprobe moves further away from the sample surface, the response amplitudeof the probe will naturally increase, giving a positive or increasingamplitude error signal. The dynamic drive feedback will increase thedrive to the cantilever to maintain tapping of the tip on the surface.When the probe moves towards the sample surface, the response amplitudeof the probe will be limited by the sample surface and forced todecrease, giving a negative decreasing amplitude error signal. Thedynamic drive feedback will decrease the drive to the cantilever toprevent it from tapping on the surface with excess force.

[0041] The amplitude error signal is an indication of the changingposition of the probe tip with respect to the sample surface. It is usedby the Z position feedback loop to maintain the probe tip in closeproximity to the sample surface. The speed of the Z feedback loop isincreased if the amplitude error signal is utilized to determine whenthe cantilever will require more drive signal amplitude in order for theZ position feedback loop to respond quickly to topographic changes.

[0042] These and other objects, features, and advantages of theinvention will become apparent to those skilled in the art from thefollowing detailed description and the accompanying drawings. It shouldbe understood, however, that the detailed description and specificexamples, while indicating preferred embodiments of the presentinvention, are given by way of illustration and not of limitation. Manychanges and modifications may be made within the scope of the presentinvention without departing from the spirit thereof, and the inventionincludes all such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

[0043] A preferred exemplary embodiment of the invention is illustratedin the accompanying drawings in which like reference numerals representlike parts throughout, and in which:

[0044]FIG. 1 is a schematic diagram illustrating an AFM according to thepresent invention including a self-actuated cantilever and feedbackcircuitry to control the cantilever in contact mode operation;

[0045]FIG. 2 is a schematic diagram illustrating an AFM according to asecond embodiment of the present invention including a self-actuatedcantilever and feedback circuitry to control the cantilever in cyclicalmode operation;

[0046]FIG. 3 is a schematic diagram illustrating a self-actuated AFMcantilever according to the present invention and a cantilever drivecircuit which modifies the quality factor (“Q”) of the cantilever;

[0047]FIG. 4 is a schematic diagram illustrating an AFM according to thepresent invention including a self actuated cantilever and feedbackcircuitry to control the cantilever in cyclical mode, and a cantileverdrive circuit for modifying the quality factor (“Q”) of the cantilever;

[0048]FIG. 5 is a schematic diagram illustrating a self-actuated AFMcantilever according to the present invention and an alternateembodiment of the cantilever drive circuit which modifies the qualityfactor (“Q”) of the cantilever;

[0049]FIG. 6 is a schematic diagram illustrating an AFM according to thepresent invention including a self actuated cantilever and feedbackcircuitry to control the cantilever in cyclical mode, and an alternateembodiment of the cantilever drive circuit for modifying the qualityfactor (“Q”) of the cantilever;

[0050]FIG. 7 is a perspective view of a probe assembly including aself-actuated cantilever having a thermal actuator integrated therewith;

[0051]FIG. 8 is a cross-sectional elevational view of an AFM accordingto another embodiment of the present invention, adapted for fluidoperation;

[0052]FIG. 9 is a schematic representation of another alternateembodiment of the present invention in which gasses are introduced tothe sample environment;

[0053]FIG. 10 is a flow diagram illustrating AFM operation when makingsingle pixel measurements;

[0054]FIG. 11 is a schematic diagram illustrating an AFM according tothe present invention, including an alternate embodiment of thecantilever dynamic drive circuit which modifies the Q of the cantileveras a function of the amplitude of the cantilever response; and

[0055]FIG. 12 is a schematic diagram illustrating an AFM according tothe present invention including a cantilever and feedback circuitry tocontrol the cantilever in cyclical mode, and a cantilever drive circuitfor dynamically controlling the drive amplitude to the cantilever.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0056] Referring to FIG. 1, an AFM 10 according to the presentinvention, which is configured for contact mode operation, is shown. AFM10 includes two feedback loops 12 and 14 that control an AFM Z positionactuator 16 and a probe assembly 18, respectively. Probe assembly 18includes a self-actuated cantilever 20 having a tip 26 that interactswith a sample during scanning. When scanning in contact mode, tip 26generally continually contacts the sample, only occasionally separatingfrom the sample, if at all. For example, at the end of a line scan tip26 may disengage the sample surface. While it scans the surface of thesample, cantilever 20 responds to the output of feedback loop 12 toultimately map the topography of the surface of the sample, as describedin further detail below.

[0057] Cantilever 20 includes a fixed end 22 preferably mounted to anAFM mount (not shown) and a free distal end 24, generally opposite fixedend 22, that receives tip 26. In operation, the interaction between tip26 and sample surface 28 causes the deflection of cantilever 20. Tomeasure this deflection, AFM 10 includes a deflection detector 30 thatmay preferably be an optical detection system for measuring thecantilever deflection by one of the following methods: (1) an opticalbeam bounce technique (see, e.g., Meyer and Amer, “Novel OpticalApproach to Atomic Force Microscopy,” Appl. Phys. Lett. 53, 1045 (1988);Alexander, Hellemans, Marti, Schneir, Elings, Hansma, Longmire, andGurley, “An Atomic-Resolution Atomic-Force Microscope Implemented Usingan Optical Lever,” Appl. Phys. Lett. 65 164 (1989)); (2) an interdigitaldiffraction grating technique (Manalis, Minne, Atalar, and Quate,“Interdigital Cantilevers for Atomic Force Microscopy,” Appl. Phys.Lett., 69 (25) 3944-6 (1996); Yoralioglu, Atalar, Manalis, and Quate,“Analysis and design of an interdigital cantilever as a displacementsensor,” 83(12) 7405 (June 1998)); or (3) by any other known opticaldetection method. These optical-based systems typically include a laserand a photodetector (neither shown) that interact according to one ofthe above techniques. When used in conjunction with very smallmicrofabricated cantilevers and piezoelectric positioners as lateral andvertical scanners, AFMs of the type contemplated by the presentinvention can have resolution down to the molecular level, and canoperate with controllable forces small enough to image biologicalsubstances.

[0058] Deflection detector 30 could also be a piezoresistor integratedinto the cantilever with an associated bridge circuit for measuring theresistance of the piezoresistor (Tortonese, Barrett, and Quate, “AtomicResolution With an Atomic Force Microscope Using PiezoresistiveDetection,” Appl. Phys. Lett., 62, 8, 834-6 (1993)). Alternatively,deflection detector 30 could be a circuit for measuring the impedance ofthe piezoelectric element of self-actuated cantilever 20, or anothersimilarly related apparatus.

[0059] With further reference to FIG. 1, AFM 10 operates at a forcedetermined by a combination of a first signal having a setpoint valueand a cantilever detection signal generated by deflection detector 30.In particular, AFM 10 includes a difference amplifier 32 that receivesand subtracts the setpoint signal from the cantilever deflection signalthereby generating an error signal. Difference amplifier 32 transmitsthe error signal to a controller 34, preferably a PID(proportional-integral-derivative) controller, of feedback loop 12.Controller 34 can be implemented in either analog or digital, and mayapply either a linear gain or a gain characterized by a more complexcomputation. In particular, controller 34 can apply a gain to the errorsignal that is defined by one or more of a proportional, an integral ora differential gain.

[0060] Controller 34, in response to the error signal, then generates acontrol signal and transmits the control signal to a piezoelectricelement 36 disposed on self-actuated cantilever 20. By controlling the Zor vertical position of piezoelectric element 36 of cantilever 20 withfeedback control signals from controller 34, AFM 10 ideally operates tonull the error signal generated by difference amplifier 32. When theerror signal is nulled, the force between tip 26 and sample surface 28is maintained at a generally constant value equal to the setpoint. Notethat, optionally, a high voltage amplifier (not shown) may be employedto increase the voltage of the control signal transmitted to cantilever20, but is not required for most applications.

[0061] The control signal applied to cantilever 20 by controller 34 offeedback circuit 12 is also input, preferably as an error signal, to asecond feedback circuit 14 such that first feedback circuit 12 is nestedwithin second feedback circuit 14. Feedback circuit 14 includes a secondcontroller 38 which, like controller 34, can be implemented in analog ordigital and may apply either a linear gain or a gain having a morecomplex computation. Controller 38 has a second input to which isapplied a comparison signal having a second setpoint value that is equalto the Z center point of the actuator that it controls, e.g., AFM Zposition actuator 16. Preferably, this setpoint is a zero coordinatevalue, thus making the cantilever control signal (the output ofcontroller 34) itself the error signal. Similar to controller 34,controller 38 (also preferably a PID controller) conditions the errorsignal (i.e., the difference of its input signals) with a gain that ischaracterized by one or more of a proportional, integral or differentialgain. Controller 38 generates a second feedback control signal that isultimately applied to Z position actuator 16 to effectively null the lowfrequency components of the control signal generated by feedback circuit12. A high voltage amplifier 40 may be employed to increase the voltageof the control signal output by controller 38 to Z position actuator 16and, for most position transducers of the scale contemplated by thepresent invention, such an amplifier 40 is required.

[0062] To operate at maximum scanning rate, the gain of the secondfeedback loop 14 which controls Z position actuator 16, is reduced tozero or some small value. As a result, at a scanning rate greater thanabout 500 μm/sec, the topography of sample surface 28 appears as thefeedback control signal applied to self-actuating cantilever 20 by firstfeedback loop 12. In this case, Z position actuator 16 may be controlledin a pre-programmed manner to follow the slope of sample surface 28 orto eliminate coupling due to the lateral scanning of tip 26.

[0063] Further, in this embodiment, the sensitivity of the self-actuatedcantilever 20 can be calibrated with the standard Z position actuator16. Sensitivity calibration is accomplished by moving the two actuators16 and 36 in opposite directions to achieve a zero net movement of thetip 26 as measured by force deflection detector 30, and comparing therespective non-zero control signals required to accomplish this zero netmovement.

[0064] Turning to FIG. 2, an AFM 50 according to another preferredembodiment of the invention, designed for TappingMode™ or cyclical modeoperation, is shown. AFM 50, like the embodiment show in FIG. 1,includes two feedback circuits (loops) 52 and 54 that respectivelycontrol self-actuated cantilever 20 of probe assembly 18 and AFM Zposition actuator 16. AFM 50 also includes an oscillator 56 thatvibrates self-actuated cantilever 20 by applying an oscillating voltagedirectly to piezoelectric element 36 of self-actuated cantilever 20. Theresulting oscillation of the cantilever 20 can be characterized by itsparticular amplitude, frequency and phase parameters. Note that AFM Zposition actuator 16 is preferably a piezo-tube actuator, and a sampleto be analyzed is disposed on the piezo-tube actuator such that movementof actuator 16 is generally normal to the scanning surface 28 of thesample.

[0065] When tip 26 is in close proximity to sample surface 28, the forceinteraction between tip 26 and sample surface 28 modifies the amplitudeof vibration in cantilever 20. Similar to the contact mode embodimentshown in FIG. 1, deflection detector 30 measures the deflection ofcantilever 20 by an optical beam bounce technique, an interdigitaldiffraction grating technique, or by some other optical detection methodknown in the art.

[0066] In operation, once detector 30 acquires data pertaining tocantilever deflection, detector 30 generates a deflection signal whichis thereafter converted to an RMS amplitude signal by an RMS-to-DCconverter 58 for further processing by loop 52. Note that,alternatively, lock-in detection, or some other amplitude, phase, orfrequency detection technique may be used as an alternative to RMS-to-DCconverter 58.

[0067] The operating RMS amplitude of the cantilever vibration isdetermined at least in part by the setpoint value. A differenceamplifier 32 subtracts a signal corresponding to the setpoint value fromthe cantilever deflection signal output by converter 58. The errorsignal generated by difference amplifier 32 as a result of thisoperation is input to controller 34. Controller 34 (again, preferably aPID controller) applies one or more of proportional, integral anddifferential gain to the error signal and outputs a correspondingcontrol signal. Controller 34 then applies this control signal topiezoelectric element 36 of self-actuated cantilever 20 to control the Zposition of cantilever 20 as the cantilever traverses varying topographyfeatures of the sample surface. By applying the feedback control signalas described, feedback loop 52 ultimately nulls the error signal suchthat, for example, the oscillation amplitude of cantilever 20 ismaintained at the setpoint value.

[0068] A summing amplifier 60 then sums the feedback control signaloutput by controller 34 with the output of driving oscillator 56 so asto apply the feedback cantilever control signal to element 36. Note thata high voltage amplifier (not shown) may be employed to increase thevoltage of the summed signal output by amplifier 60 and applied topiezoelectric element 36 of cantilever 20, but is not required.

[0069] The control signal applied to summing amplifier 60 from thecontroller 34 is also input to controller 38 as the error signal ofsecond feedback loop 54 such that first feedback loop 52 (similar tofeedback loop 12 of the contact mode embodiment of FIG. 1) is nestedwithin second feedback loop 54. Controller 38 has a second input thatreceives a comparison signal having a second setpoint value that isequal to the Z center point of the actuator that it controls, e.g., theAFM Z actuator 16. Preferably, this setpoint value is a zero coordinatevalue such that the cantilever control signal is itself the errorsignal. Controller 38 applies one or more of proportional, integral anddifferential gain to the error signal and outputs a correspondingcontrol signal for controlling Z position actuator 16, and therefore theZ position of the sample. This control of the Z position of the sampleoperates to effectively null the low frequency components of theself-actuated cantilever control signal generated by feedback circuit52. Note that a high voltage amplifier 40 may be employed between theoutput of controller 38 and the input of Z position actuator 16 toincrease the voltage of the control signal applied by controller 38 to Zposition actuator 16, and is required for most position transducers ofthe scale contemplated by the present invention.

[0070] During fast scanning operation, as in the previously describedembodiment, the gain of second feedback loop 54, which controls Zposition actuator 16, is preferably reduced to zero or some small value.In this cyclical mode case, Z position actuator 16 may be controlled,for example, in a pre-programmed manner, to either follow the slope ofsample surface 28 or to eliminate coupling due to the lateral scanningof tip 26. To the contrary, when the gain of second feedback loop 54 isoptimized, the control signal output by loop 54 is indicative of thesample topography. As a result, depending upon scanning rate, thefeedback cantilever control signals output by loop 52, and correspondingto particular lateral coordinates, are indicative of the topography ofsample surface 28. These signals can then be further processed to createan image of the sample surface.

[0071] The bandwidth of the amplitude detection of the cantilever incyclical mode or in non-contact mode is limited by the frequency widthof the mechanical resonance peak of the cantilever, which is defined bythe 3 dB roll-off frequencies. In particular, the 3 dB roll-off is equalto f/2Q, where f is the center frequency of the resonance peak and Q isthe quality factor of the cantilever resonance peak. As such, the widthof the resonance peak is proportional to the quality factor Q of theresonance peak.

[0072]FIG. 3 shows schematically how the Q (quality factor of thecantilever resonance peak) of self-actuated cantilever 20 can bemodified using a deflection feedback technique. Generally, an activedamping feedback or cantilever drive circuit 62 modifies the oscillatingvoltage output by a driving oscillator 66 (and applied directly topiezoelectric element 36 of cantilever 20) to optimize the bandwidth ofamplitude detection. Active damping circuit 62 utilizes a deflectiondetector 30 that, as described with respect to FIGS. 1 and 2, ispreferably an optical detection system including a laser and aphotodetector, and which measures cantilever deflection by an opticalbeam bounce technique or another conventional technique. Alternatively,as in the previously described embodiments, deflection detector 30 couldbe (1) a piezoresistor integrated into cantilever 20 with an associatedbridge circuit for measuring the resistance of the piezoresistor, or (2)a circuit for measuring the impedance of the piezoelectric element 36 ofself-actuated cantilever 20.

[0073] As it senses a deflection of cantilever 18, deflection detector30 transmits a corresponding deflection signal to a damping element ofactive damping circuit 62. In one preferred embodiment, the dampingelement is a phase shifter 64 that advances or retards the phase of thesensed deflection signal by 90 degrees. This phase shift acts as adamping component of the oscillatory motion of cantilever 20 to modifythe Q of the mechanical resonance of the cantilever. The phase-shifteddeflection signal is then summed with the output of a driving oscillator66 by a summing amplifier 68.

[0074] The relative gain of the oscillator signal amplitude to the phaseshifted deflection signal determines the degree to which the Q of thecantilever resonance is modified, and therefore is indicative of theavailable bandwidth. Note that the ratio of the two summed signals canbe scaled at summing amplifier 68 to determine the extent to which thecantilever resonance is modified. Alternatively, a gain stage 65 couldbe inserted between phase shifter 64 and summing amplifier 68 to scalethe phase-shifted signal and obtain the resonance modifying data.

[0075] Notably, as the operator turns the gain up to achieve optimumoperation, the cantilever may be driven to undesirably operate at one ofits harmonics. As a result, due to this change or due to the actuator ofthe self-actuating probe being imperfect (e.g., the probe may have aresonance at about 50 kHz), the actuator may feed back positively anddrive the cantilever so the cantilever ends up oscillating at afrequency other than at the desired operating frequency. This acts as alimit to how much damping can be realized. In an effort to avoidgenerating this positive feedback, a bandpass filter 63 centered aroundthe peak of desirable operation, and preferably disposed at the outputof the cantilever drive circuit 62 (see FIGS. 3-6) can be included so asto insure that the system damps the peak, thus allowing the system toachieve damping up to a factor of, for example, a hundred, rather than amaximum factor of fifty with the above-described system 80.

[0076] In sum, by actively damping the oscillation voltage to modify theQ as described above, damping circuit 62 ideally optimizes the bandwidthof the response of the cantilever 20. As a result, the AFM can maximizescan rate, yet still maintain an acceptable degree of force detectionsensitivity.

[0077]FIG. 4 shows an AFM 80 according to an alternate embodiment of thepresent invention incorporating the features of AFM 50 (cyclical modeconfiguration—FIG. 2), including two nested feedback loops 82 and 54,with the features of active damping circuit 62 (FIG. 3) to modify the Qof cantilever 20 in fast scanning cyclical mode operation. By activelydamping the resonance of cantilever 20 with feedback signals output bycircuit 62, the force detection bandwidth rises proportionally with acorresponding decrease in the Q. By combining a decrease in Q with thecontrol features of AFM 50 (FIG. 2), AFM 80 realizes much greater loopbandwidth in cyclical mode, thus achieving much greater (and much morecommercially viable) throughput per machine.

[0078] With further reference to FIG. 4, AFM 80 operates as follows.Initially, the deflection signal obtained by deflection detector 30during a scanning operation is phase shifted by phase shifter 64 ofactive damping circuit 62. As noted above, the phase of the deflectionsignal is advanced or retarded by 90 degrees such that it acts as adamping component of the oscillatory motion of cantilever 20, thusmodifying the cantilever Q. The phase-shifted deflection signal is thensummed with the output of oscillator 66 by summing amplifier 68.

[0079] The ratio of the two summed signals can be scaled at summingamplifier 68 to determine the extent to which the cantilever resonanceis modified. Alternatively, as described in connection with FIG. 3, again stage 65 can be inserted between the phase shifter and the summingamplifier to scale the phase-shifted signal. The output of summingamplifier 68 is then further amplified (with amplifier 70) to a suitablevoltage for driving piezoelectric element 36 of self-actuated cantilever20.

[0080] With continued reference to FIG. 4 and the more specificoperation of AFM 80, the output of amplifier 70 drives self-actuatedcantilever 20 at a frequency equal to that of the natural resonance ofcantilever 20, wherein the Q of the driving frequency is modified byactive damping circuit 62 to increase overall loop bandwidth. Thischange in Q increases the speed of data collection, for example, viascanning/imaging. Moreover, in an effort to avoid generating undesirablepositive feedback, a bandpass filter 63 centered around the peak ofdesirable operation, and preferably disposed at the output of thecantilever drive circuit 62 (see FIGS. 3-6) can be included so as toinsure that the system damps the peak. Notably, because thepiezoelectric element 36 disposed on cantilever 20 is used to drivecantilever 20 at its resonant frequency, the oscillating voltage in thisembodiment can be applied directly to cantilever 20 without introducingextraneous mechanical resonance's into the system.

[0081] When the tip 26 is in close proximity to sample surface 28, theforce interaction between tip 26 and sample surface 28 modifies theamplitude of vibration in cantilever 20. The deflection signal generatedby the deflection detector 30 in response to a detected change in theamplitude of vibration is then converted to an RMS amplitude signal byRMS to DC converter 58 to facilitate further processing. Notably,lock-in detection or some other amplitude, phase, or frequency detectiontechnique may be used in place of RMS to DC converter 58.

[0082] Similar to AFM 50, the operating RMS amplitude of the cantilevervibration is determined (at least in part) by the setpoint value, whichis subtracted from the cantilever deflection signal by differenceamplifier 32. The error signal generated by difference amplifier 32 isinput to controller 34. Controller 34 applies one or more ofproportional, integral and differential gain to the error signal andcontrols piezoelectric element 36 of self-actuated cantilever 20 to nullthe error signal, thus ensuring that the amplitude of cantileveroscillation is kept generally constant at a value equal to the setpoint.A high voltage amplifier (not shown) may be employed to increase thevoltage of the signal to cantilever 20, but is not required.

[0083] The control signal transmitted by controller 34 to cantilever 20is also input to controller 38 of second feedback loop 54 such thatfirst feedback loop 82 is nested within second feedback loop 54.Preferably, the second setpoint input to controller 38 is a zero valueassociated with AFM actuator 16, in which case the cantilever controlsignal is itself the error signal conditioned by controller 38. Again,PID controller 38 applies one or more of proportional, integral anddifferential gain to the error signal for ultimately controlling Zposition actuator 16 to null the low frequency components of the controlsignal applied to the self-actuated cantilever, when scanning at anoptimum rate. Further, as highlighted above, a high voltage amplifier 40may be employed to increase the voltage of the control signal applied toZ position actuator 16, and is required for most position transducers ofthe scale contemplated by the present invention.

[0084] In sum, AFM 80 combines an AFM Z actuator 16 with a self-actuatedcantilever 20 in a manner that allows both high speed imaging andaccurate Z position measurement by decreasing the effective Q ofcantilever 20 with damping circuit 62. Damping circuit 62 activelymodifies the oscillating voltage signal output by oscillator 66, whilepreserving the sensitivity of the natural resonance, to insure that thebandwidth of the cantilever response is optimized. Further, dependingupon the particular sample topography and the scan rate, the topographycan be mapped by monitoring one of the feedback control signalsindependent of the other.

[0085] In an alternative embodiment to the deflection feedback circuitryshown in FIG. 3, a cantilever drive circuit 109 includes a dampingelement that comprises a differentiator 110, as shown in FIG. 5.Differentiator 110, in conjunction with an adjustable gain stage 116,provides a signal that is a very close approximation to the dampingcomponent of the cantilever oscillation so as to change the system Q.More particularly, differentiator 110 differentiates the deflectionsignal sensed by deflection detector 30 during operation. Thedifferentiated signal is then applied to the gain stage 116. The gainapplied by gain stage 116 is adjusted to selectively modify the Q of thecantilever so as to realize a desired Q, Q_(new).

[0086] Next, the differentiated deflection signal is applied to summingamplifier 68 and summed with the output of driving oscillator 66 toprovide the modified oscillating voltage, similar to active dampingcircuit 62 described previously. Prior to applying the modifiedoscillating voltage to cantilever 20, an amplifier 70 amplifies theoutput of summing amplifier 68 to a suitable voltage for drivingpiezoelectric element 36 of self-actuated cantilever 20. Duringoperation, the output of amplifier 70 drives self-actuated cantilever 20at the mechanical resonance of cantilever 18. In addition, althoughdifferentiator 110 can be implemented digitally, preferably it is ananalog differentiation circuit.

[0087] Notably, differentiator 110 (with appropriate gain provided bygain stage 114) can be used not only for active damping, but for activeenhancement (i.e., to increase the Q) as well. For example, whenoperating in fluid, the viscous forces present in the system cansignificantly damp the system response. Therefore, to counter thedamping effects of these forces, differential gain can be used toincrease the Q. Although such operation can decrease operation speed,the sensitivity of the response is enhanced, thus facilitating reliabledata collection. Moreover Q enhancement allows the AFM to output alarger data signal that is easier to process. Among other applications,active enhancement is particularly useful when imaging soft samples inair because the increased force sensitivity allows greater control ofthe drive voltage (e.g., greater control over the tip-sampleinteraction), thus minimizing the chance of damaging the sample.

[0088] Cantilever drive circuit 109 includes two additional branches,one including an integrator 112 having an output coupled to acorresponding amplifier 118 to provide integral gain, while the othercomprises an amplifier 114 that provides proportional gain. Integrator112 and the associated amplifier 118 process the cantilever deflectionsignal so as to tune the feedback response in conventional fashion. Theproportional gain provided by amplifier 114, on the other hand, can beused to actively modify the response of the cantilever. In particular,amplifier 114 applies proportional gain, preferably to change theresonant frequency of the cantilever, which, as discussed previously, isthe preferred frequency of operation. Cantilever drive circuit 109 willemploy proportional gain if, for example, the system experiencessignificant noise at the operational resonant frequency. Such noise cansignificantly compromise data collection and imaging capabilities suchthat, by shifting the resonant frequency with proportional gain,cantilever drive circuit 109 permits the AFM to operate at a frequencywhere noise is not a significant limitation.

[0089] Amplifiers 114, 116 and 118 are preferably independentlyadjustable with positive and negative polarities. Amplifiers 114, 116,118 are controlled either manually, typically as the user observes theAFM output, or automatically via, for example, a central processing unit120 or microprocessor, which computes the proper gain in response to thedesired Q, preferably input by the operator. CPU 120 can use analgorithm embedded in memory to intelligently apply differential,proportional and integral gain in response to analyzing the deflectionsignal, thus optimizing AFM operation in terms of speed and datacollection quality, as described previously.

[0090] To determine the proper amount of gain to be applied for adesired response, the AFM is modeled. According to the preferredembodiment, the feedback system shown in FIG. 5 can be characterized bythe following equation, $\begin{matrix}{\frac{V_{o}}{V(\omega)} = \frac{\gamma \quad k\quad {{\eta\chi}(\omega)}}{1 - {\gamma \quad k\quad {{\eta\chi}(\omega)}{G(\omega)}}}} & {{Eqn}.\quad 1}\end{matrix}$

[0091] wherein χ_((ω)) is the cantilever response, γk is the response ofthe piezoelectric element, (zinc oxide for example), η is the responseof the deflection detector 30 (e.g., a photodiode sensor) and G(ω) isthe gain to be applied. The response of the piezoelectric element (γk)and the response of the photodiode (η) are predetermined according tothe type of cantilever used and therefore define constants in Equation1.

[0092] The cantilever can be modeled as a basic second-order systemhaving a frequency-based response characterized by the followingequation, $\begin{matrix}{{\chi (\omega)} = \frac{\omega_{o}^{2}/k}{\omega_{o}^{2} - \omega^{2} + \frac{i\quad {\omega\omega}_{0}}{Q}}} & {{Eqn}.\quad 2}\end{matrix}$

[0093] wherein ω_(o) is the resonant frequency of the cantilever, ω isthe operational frequency of the system, k is the spring constant, and Qis the native Q of the system (a quantity that is measured duringoperation). Therefore, the system response becomes, $\begin{matrix}{\frac{V_{o}}{V(\omega)} = \frac{{\gamma\eta\omega}_{o}^{2}}{\left( {\omega_{o}^{2} - \omega^{2}} \right) + \frac{i\quad {\omega\omega}_{o}}{Q} - {{\gamma\eta\omega}_{o}^{2}{G(\omega)}}}} & {{Eqn}.\quad 3}\end{matrix}$

[0094] where G(ω) can be any physically realizable function, real orimaginary, so as to provide proportional, differential, integral, ω²,etc. gain.

[0095] More particularly, the expression$\frac{i\quad {\omega\omega}_{0}}{Q}$

[0096] is the term representative of differentiator 110 and, therefore,is the term that is manipulated to modify cantilever damping. To modifycantilever damping, i.e., to modify the Q of the cantilever, the gain isset according to the following equation, $\begin{matrix}{{G(\omega)} = {i\frac{\omega}{\omega_{o}}\frac{1}{\gamma\eta}\left( {\frac{1}{Q} - \frac{1}{Q_{new}}} \right)}} & {{Eqn}.\quad 4}\end{matrix}$

[0097] where, again, Q is the native Q, and Q_(new) is the desired Q foroptimum operation.

[0098] When substituting the gain (Eqn. 4) into the system response asdefined by Eqn. 3, the response remains the same except that the nativeQ is replaced by the desired Q, Q_(new). In particular, the systemresponse becomes, $\begin{matrix}{\frac{V_{o}}{V(\omega)} = \frac{{\gamma\eta\omega}_{o}^{2}}{\left( {\omega_{o}^{2} - \omega^{2}} \right) + \frac{i\quad {\omega\omega}_{o}}{Q_{new}}}} & {{Eqn}.\quad 5}\end{matrix}$

[0099] As an example, in computing the gain as defined in Eqn. 4, we canassume that the phase is 90° and that ω_(o) equals ω_(o) (which ispreferably the case where the AFM is operated at the resonant frequencyof the cantilever). As a result, the gain becomes, $\begin{matrix}{{{Abs}(G)} = {\frac{1}{{\gamma\eta}\quad Q} - {\frac{1}{\gamma\eta} \cdot \frac{1}{Q_{new}}}}} & {{Eqn}.\quad 6}\end{matrix}$

[0100] For a Q=300 Å/V, γ=200 Å/V and η=0.33 mV/Å, the gain is equal to0.05-14.9/Q_(new). Q_(new) can be input manually by the user, or it canbe intelligently selected according to an algorithm embedded in CPU 120.

[0101] For example, an algorithm for selecting a Q using computer 120takes into consideration the spatial frequency of the sample topography,the scan size, and the scan rate which are input by the operator. Theproduct of the scan size and the scan rate is the tip velocity. In onepreferred embodiment, the algorithm is an open loop algorithm that makesan assumption about the sample topography and then scales the desired Q,Qnew, for the selected tip velocity. Notably, because any AFM image isultimately a convolution of the sample topography and the probe tip, alimit to the spatial frequency of the topography is considered to be thegeometry of the probe tip. Alternatively, a closed loop algorithmincludes a subroutine of a gain setting algorithm for the Z feedbackloop. One such known algorithm selects the optimum integral andproportional gain of the Z feedback loop by maximizing theautocorrelation function of the trace and retrace scan lines.Preferably, once this routine is executed, a damping subroutine uses thefeedback loop error signal (RMS-setpoint) to determine if enough gain isbeing used (i.e., the routine determines whether the error signal isbelow a predetermined threshold). To achieve more gain, the Q isdecreased, and then the gain setting routine is reinitiated. If the Qreaches a predetermined minimum value, then the gain setting routineoperates to reduce the scan rate for optimum operation.

[0102] In general, computer 120 outputs a control signal that iscommunicated to one of the gain stages 114, 116, 118 for applying theappropriate gain to optimize AFM operation. To modify the Q of thecantilever, the response of both the piezoelectric element 20 and thedeflection detector 30 are set according to the type of cantilever used.Based on the desired Q (i.e., Q_(new)), computer 120 generates a controlsignal and transmits the control signal to, for example, gain stage 114so as to cause gain stage 114 to apply the appropriate gain to thedetected deflection signal to increase AFM operating speed, thusreducing Qnew and increasing the damping or drag. Alternatively, gaincan be computed so as to enhance the Q and therefore decreasing thedamping. In this alternative, the AFM is slowed correspondingly;however, the signal-to-noise ratio, as well as the force sensitivity,increases, thus providing advantages in terms of increased control overtip-sample interaction and operational convenience.

[0103] Overall, Q modification using phase shifting (FIGS. 3 and 4) issimilar to using differential gain (FIGS. 5 and 6) to modify the Q.However, phase shifting behaves like differential gain only in a narrowbandwidth when the phase shifter is adjusted correctly (i.e., 90°). Whenthe phase shifter is out of adjustment, phase shifting behaves like alinear combination of differential and proportional gains, thus shiftingthe resonant frequency as well as modifying the quality factor, Q of thecantilever. Because AFM cantilevers typically have some variation intheir natural resonant frequencies, the phase shifter 64 (FIGS. 3 & 4)must be adjusted whenever the cantilever is changed, which can be quiteoften. With separate differential and proportional gain, cantileverdrive circuit 109 modifies the damping and the resonant frequencyindependently without significant sensitivity to different naturalresonant frequencies of different cantilevers.

[0104] Similar to FIG. 4, FIG. 6 shows an AFM 130 according to analternate embodiment of the present invention incorporating the featuresof AFM 50 (cyclical mode configuration—FIG. 2), including two nestedfeedback loops 132 and 54. AFM 130 also includes the features ofcantilever drive circuit 109 (FIG. 6) to modify the Q of cantilever 20in fast scanning cyclical mode operation. Alternatively, by combiningthe control features of AFM 50 (FIG. 2) with active enhancement providedby cantilever drive circuit 109, AFM 130 can, for example, increase theforce sensitivity to facilitate imaging soft samples even thoughthroughput may decrease. As described previously in conjunction withFIG. 5, enhancing the Q is particularly useful when operating in fluid,e.g., when imaging biological samples, because the viscous environmentcan have a detrimental damping effect on the Q. Overall, AFM 130 ispreferably operated as fast as possible without significantlycompromising force sensitivity.

[0105] Referring specifically to FIG. 6, AFM 130 is similar to AFM 80except that cantilever drive circuit 109 is substituted for dampingcircuit 62. As a result, AFM 130 has the same capabilities of AFM 80.However, in addition, AFM 130 provides proportional and integral gain,as well as active Q enhancement which is implemented with applieddifferential gain, as described above in conjunction with FIG. 5.

[0106] When changing the Q of the cantilever, the resonant or peakamplitude of cantilever response also changes. Generally, the ratiobetween the amplitude and the Q will remain constant such that if youdecrease the Q by a factor of two, the amplitude will correspondinglydecrease by a factor of two. Notably, it is often times desired to holdthe amplitude constant while changing the cantilever Q to avoid havingto constantly re-scale the drive to either observe the change in Q, oruse the actively modified response. Re-scaling the drive can be timeconsuming and often times is difficult. However, implementing a systemthat holds peak amplitude constant while changing the Q is notintuitive. This is due to the fact that, unlike the relationship betweenthe amplitude and the Q, the amount one needs to increase the cantileverdrive signal does not scale directly with the change in Q.

[0107] More particularly, turning again to FIG. 5, cantilever drivecircuit 109 can be used in conjunction with computer 120 to compute theappropriate scale factor for the drive when changing the Q. As discussedpreviously with respect to Eqn. 1, each cantilever has a gain associatedwith the device itself (piezoelectric (η) and mechanical (γk)), and withthe sensor system. Again, Eqn. 1 represents the relationship between thedesired Q, Q_(new), and the associated necessary gain, G, required toachieve the Q_(new). Because the AFM is preferably operated atresonance, we can assume the drive frequency is approximately equal tothe resonant frequency such that the relationship defined in Eqn. 5becomes,

V _(o) =γηQ _(new) V(ω)  Eqn. 7

[0108] and the gain defined in Eqn. 4 becomes, $\begin{matrix}{{G(\omega)} = {\frac{1}{\gamma\eta}\left( {\frac{1}{Q} - \frac{1}{Q_{new}}} \right)}} & {{Eqn}.\quad 8}\end{matrix}$

[0109] The next step in determining the appropriate drive scale factoris to solve for Q_(new) in Eqn. 8 which becomes, $\begin{matrix}{Q_{new} = \frac{Q}{\left( {1 - {{\gamma\eta}\quad {QG}}} \right)}} & {{Eqn}.\quad 9}\end{matrix}$

[0110] When substituting the quantity shown in Eqn. 9 into Eqn. 7, thesystem response becomes, $\begin{matrix}{V_{o} = {{\frac{{\gamma\eta}\quad Q}{\left( {1 - {{\gamma\eta}\quad {QG}}} \right)} \cdot {V(\omega)}} = {{\beta (G)} \cdot {V(\omega)}}}} & {{Eqn}.\quad 10}\end{matrix}$

[0111] As a result, when varying the gain to alter the Q, if it isdesired that V_(o) be held constant, the appropriate amount to scale thedrive, V(ω), is by $\frac{1}{\left( {\beta (G)} \right)}$

[0112] or by, $\begin{matrix}{{{Drive}\quad {scale}\quad {factor}} = {\left( \frac{1 - {\gamma \quad \eta \quad {QG}}}{{\gamma\eta}\quad Q} \right) = {\frac{1}{\left( {{\gamma\eta}\quad Q} \right)} - G}}} & \text{Eqn.~~11}\end{matrix}$

[0113] Notably, γηQ is$\frac{V_{{r\quad m\quad s}\quad}}{V_{drive}},$

[0114] i.e., the system response $\frac{V_{drive}}{V_{out}},$

[0115] and is independent of other circuitry, including the activecontrol circuitry of the present invention. In addition, G is nominallypositive, such that for damping, the gain is negative. This calculationcan be implemented with analog electronics, a DSP, a microprocessor or,as shown in FIG. 5, a CPU 120. In this latter case, an output ofcomputer 120 transmits a drive scale signal indicative of the drivescale factor and applies the drive scale signal to a multiplier 122.Multiplier 122 multiplies the drive scale factor by the output ofoscillator 66 so as to scale the output.

[0116] It should be highlighted that the above equations including thedrive scale factor depicted in Eqn. 11, do not need to be followed. Abrute force approach could be followed in which the peak amplitude isfound and scaled. Performing a frequency sweep and analyzing the resultscan also produce these results, even though the preferred embodiment isdescribed above. A practical “brute force” method for maintainingamplitude while changing the Q would be to first measure the RMSamplitude of the cantilever oscillation for a given drive amplitude.Thereafter, the operator can iteratively increase the damping gain, andthen the drive amplitude, to arrive at the same RMS amplitude as thepreviously measured value. These steps are then repeated until a targetdrive amplitude is reached. In this case, the target is the desiredchange in Q_(A) (i.e., ΔQ times the original drive amplitude).

[0117] Notably, although the embodiments shown in FIGS. 3-6 aredescribed in conjunction with cyclical mode operation, cantilever drivecircuits 62 (FIG. 3) and 109 (FIG. 5) can be used in any mode (e.g.,contact) to modify damping, alter the resonance, etc.

[0118] Turning to FIG. 7, an alternate embodiment of the presentinvention includes one in which the standard AFM Z position actuator 16(e.g., a piezo-tube actuator) of the previous embodiments is replacedwith a thermally responsive actuator integrated with the self-actuatedcantilever. More particularly, the alternate embodiment includes a probeassembly 140 including a self-actuated cantilever 142 having 1) a firstend 144 attached to an AFM substrate 146, 2) an elongated portion 148,and 3) a second, distal end 150 that includes a tip 152 for scanning thesurface 28 (see, e.g., FIG. 4) of a sample. Self-actuated cantilever 142also includes a Z-positioning element 154 disposed thereon.

[0119] This embodiment of the invention operates on the principal ofdissimilar expansion coefficients between cantilever 142. For instance,the cantilever 142 may be formed from a silicon material, and theZ-positioning element 154 may be formed from zinc oxide. In thepreferred embodiment of the invention, a thermal actuator, e.g., aresistive heater 156, is integrated with the cantilever by using, e.g.,a doping process.

[0120] In operation, by heating the thermal actuator (i.e., theresistive heater 156), self-actuated cantilever 142 acts as a bimorph.Specifically, the different coefficients of thermal expansion of siliconcantilever 142 and zinc oxide Z-positioning element 154 cause cantilever142 to act as a bimorph when heated. The effect of this response is mostprominent at region 158 of cantilever 142. Notably, similar to the Zposition actuator 16 (piezo-tube Z actuator) of the previousembodiments, probe assembly 140 (and particularly the thermal actuator)can provide highly accurate imaging at relatively low scanning rates.When operating at slower imaging rates (e.g., less than 500 μm/sec), thezinc oxide element 154 is used as a reference for the thermal actuator,the thermal actuator being controlled by the feedback signal from, e.g.,control loop 54 (FIG. 4). Further, the piezoelectric effect of zincoxide Z positioning element 154 provides fast actuation of thecantilever for faster imaging rates.

[0121] Overall, by substituting the thermal actuator for the standardAFM piezo-tube Z actuator, the vertical range of operation of theself-actuated cantilever is increased, thus providing an effectivealternative for imaging samples that have a topography that demands ahigher range of vertical operation. Hence, while the actuator of theself-actuated cantilever of the previously-described embodimentspreferably can cause movement of the cantilever over a rangeapproximately equal to 2-5 μm in the Z direction and a standard piezotube actuator operates over typically a 5-10 μm range, the thermalactuator shown in FIG. 7 can cause cantilever movement over a rangeapproximately equal to 20-100 μm. Note that, although this alternativeembodiment is described as preferably utilizing zinc oxide as thepiezoelectric element, any material having suitable piezoelectricproperties to provide Z positioning of the self-actuated cantilever 142as described herein can be used.

[0122] Next, with reference to FIG. 8, an AFM 160 particularly adaptedfor imaging the surfaces of biological substances is shown. AFM 160includes a piezoelectric self-actuated cantilever 162 having apiezoelectric element 164 disposed thereon and a tip 166 that interactswith a sample 168. The sample 168 is generally immersed in a pool offluid 170 contained by a fluid cell 172. Some advantages with such asystem include elimination of capillary forces and the reduction of Vander Waals forces, particularly when analyzing and imaging biologicalsamples.

[0123] In this embodiment, the integrated high-speed actuator ofcantilever 162 replaces a conventional (e.g., piezo-stack) tip/sampleactuator used by a typical biological AFM, thus enhancing the bandwidthof the mechanical system, as described previously. Fluid cell 172 isformed, in part, using an AFM mount 174 having ports 176, 178 forinputting and dispensing fluid 170, respectively. Mount 174 also servesas a support to which a fixed end of cantilever 162 is attached. A stage179 is configured to accommodate sample 168 and comprises 1) a topsurface 184 that defines a portion of fluid cell 172 and 2) a cavitythat receives the fluid 170 and the sample 168. O-rings 180 are disposedbetween a notched portion 181 of a bottom surface 182 of mount 174 andthe top surface 184 of stage 179 to seal fluid cell 172 from thesurrounding environment. Also, the piezoelectric (e.g., ZnO) element 164is micromachined and therefore very small and very fast. For example,the resonance of a ZnO cantilever is approximately one hundred timesgreater than the resonance of a bulk piezo-tube actuator. For a givenoperational condition in the so-called contact mode, any increase inactuator resonant frequency will increase data acquisition/imaging speedin the same proportion.

[0124] As noted above, the Q of the cantilever resonance is damped bythe viscous environment in which this embodiment of the inventionoperates, thus lessening the bandwidth limitations caused by a large Q(discussed above). Nevertheless, these speed advantages are countered bythe increased drive oscillation required to operate the dampedcantilever.

[0125] In operation, the resonant nature of the cantilever 162 storesthe excitation energy and amplifies the movement of the tip 166. Thequality factor (Q) is representative of this resonant amplification andis dependent on the damping in the resonant system. In fluid, whereviscous forces are much greater than in air, the Q can dropsignificantly. With this limitation on resonant amplification, thesystem must excite the cantilever 162 almost the same amount as thedesired tip amplitude in order to drive the cantilever at its resonance.For known systems which excite the cantilever resonance with a piezotubeor piezo-stack actuator located beneath the cantilever die, the entirepiezo-stack and cantilever die are moving distances commensurate withthe tip movement. Driving the cantilever in this fashion excitesresonance's in fluid cell 172, e.g., due to acoustic excitation, thusdisrupting imaging capabilities. One preferred embodiment of the presentinvention substantially subverts this problem by using the piezoelectricelement 164 of cantilever 162 to excite the cantilever beam. Thisconstruction integrates the entire oscillating excitation onto the AFMcantilever 162 and, therefore, virtually eliminates the acousticexcitation of the fluid cell 172.

[0126] During operation in fluid, in contrast to the previouslydescribed embodiments, the electrodes (not shown) coupled to thesubstrate of self-actuated cantilever 162 will potentially interfacewith fluid 170. This fluid/electrode interaction exposes the electricalsystem of AFM 160 to a high risk of short. Therefore, the electrodesshould be passivated, e.g., insulated from fluid 170. Preferably, aninsulating layer 167 is deposited generally over the entire cantileverstructure, usually as a final step in the fabrication of cantilever 162.Depending upon the process employed, the insulating layer 167 can beremoved from the apex of tip 166. Preferably because the design andcomposition of the tip 166 affects imaging resolution, whatever thepassivation process, care should be taken to ensure that the insulatinglayer 167 does not cover the apex of the tip 166 to optimize imagingresolution.

[0127] Insulators usable as layer 167 include silicon nitride, silicondioxide, and polymers including PMMA, photoresist, RTV of any viscosityand polyimide. During cantilever fabrication, nitride and oxide may bedeposited on cantilever 162, preferably by either chemical vapordeposition (CVD), low pressure CVD or plasma enhanced CVD.Alternatively, sputtering or evaporation techniques may be used todeposit such insulators. On the other hand, polymers preferably aredeposited by spin coating or vapor phase deposition.

[0128] Another equally viable passivation technique is “shadow masking”the apex of tip 166 and spraying-on one of various polymers includingPMMA, dissolved TEFLON®, photoresist, or PDMS (polydimethylsiloxaneelastomer). The sprayer used in such a process can be, for example, acommercial air-brush, and the shadow mask can be a micropipette or apulled pipette. Alternatively, cantilever 162 can be passivated bydipping the entire probe, except for the tip 166, into PMMA,photoresist, TEFLON® or PDMS, and then allowing the device to cure.Notably, the two methods described immediately above are best performedonce the cantilever 162 is mounted onto a robust substrate. Further, thewire bonds (not shown) which connect the cantilever die to thesubstrate, and all other contacts to outside leads are preferably coatedwith an insulator such as Dow Corning 3140RTV.

[0129] The process for depositing the insulating layer 167 must becompatible with the specialized process for forming the integratedpiezoelectric actuator of cantilever 162. In particular, the insulatinglayer should be deposited on the cantilever 162 with a controlled stressbecause the film typically creates a bimorph with the cantilever whichcan cause unwanted curvature in the device. In fact, if this stress isnot controlled, the stress could potentially “rip” the cantilever 162from its base. There are a variety of conventional methods to controlthe stress when passivating the cantilever with either a deposited filmor a polymer film. For deposited films, temperature, gas ratios,pressures, power (when utilizing plasma deposition), etc. areappropriately varied to control the final film stress. The finalparameters depend on the specifications of the film and the equipmentbeing used. Similarly, polymer film stress can be controlled by varyingapplication temperature, rate of cure, polymer structure, etc. Theseparameters are altered in conventional fashion.

[0130] According to another preferred embodiment, the AFMs describedherein can be operated in a gaseous environment. In particular,corrosive, reactive or otherwise contaminating gases can be introducedto the AFM platform so as to perform, for example, real-time observationof chemical reactions between the gas and the sample. Similar tooperation in fluid, the AFM cantilever is passivated as described aboveto maintain reliable cantilever operation. Without passivating thecantilever, the corrosive gasses can damage the cantilever or, at least,have a detrimental affect on cantilever operation. One method ofintroducing a gas includes enclosing the entire AFM in a sealed chamber41 (FIGS. 4 and 6) and introducing the gas within the chamber.Alternatively, as shown in FIG. 9, gasses can be supplied to an AFM 190via unconstrained blowing of a compressed gas from a nozzle 198 towardssample 196. Yet another alternative is to use a fluid cell, such as thatshown in FIG. 8 and described above, except a gas is introduced at inlet176 rather than a liquid. According to this latter alternative, thechemical reaction is isolated within the fluid cell, which may berequired for some applications.

[0131] Although the preferred embodiments have been generally describedas apparatus and methods for imaging the surface of a sample, thetechniques described herein can be implemented for single pixelmeasurements. Rather than imaging, i.e., acquiring and conditioning datafrom a scan line or a scan area containing many pixels, the AFM isoperated to obtain data pertaining to a single pixel or point associatedwith the sample. In particular, the tip is oscillated perpendicularly tothe sample, as various measurements are made throughout each oscillationcycle. More particularly, turning to FIG. 10, a method 200 of collectingdata for a single pixel measurement includes, after initialization andstart-up at Step 202, beginning a data acquisition cycle to cause thetip to move toward the sample at Step 204. As the tip approaches thesample, tip-sample interaction is monitored. In particular, at Step 206,the attraction forces between the tip and sample are measured and storedfor further analysis. Then, during a second part of the cycle, the tipcontacts the sample surface and, at Step 208, the degree to which thesample “deforms” is measured. At Step 210, the system determines thecompliance of the sample under test and stores the data. Finally, atStep 212, a third part of the cycle causes the tip to pull away from thesample, and adhesion forces are measured and bond strength isdetermined. The method 200 then returns operation of the system back toStep 204 to collect data for additional cycles relating to the same oranother pixel. Overall, the measurements made during one (or more)cycles can be collected and processed to create a profile of theproperties of the sample.

[0132] Next, FIG. 11 shows schematically how the imaging dynamics aremodified by an alternative active drive technique. Generally, an activedamping feedback or active driving circuit 250 modifies the oscillatingvoltage output of a driving oscillator 252 (which is preferably applieddirectly to piezoelectric element 36 of cantilever 20) to optimize thebandwidth of amplitude detection. Cantilever driving circuit 250utilizes a deflection detector 254 that, as described previously, ispreferably an optical detection system including a laser and aphotodetector, which measures cantilever deflection by an optical beambounce technique or another conventional technique. Alternatively, as inthe previously described embodiments, deflection detector 254 could be(1) a piezoresistor integrated into cantilever 20 with an associatedbridge circuit for measuring the resistance of the piezoresistor, or (2)a circuit for measuring the impedance of the piezoelectric element 36 ofself-actuated cantilever 20.

[0133] In operation, as it senses a deflection of cantilever 18,deflection detector 254 transmits a corresponding deflection signal toan RMS-to-DC detector 256 of active driving circuit 250. Then, theamplitude setpoint is subtracted from the RMS amplitude signal bydifference amplifier 258 to generate an amplitude error signal. Theamplitude error signal is then processed by an amplitude detectioncircuit 259. Amplitude detection circuit 259 includes a multiplier gainstage 260 adapted to scale the error signal and generate a modifiedamplitude signal, where a select amount of gain for the optimal amountof cantilever dynamic drive feedback is applied to the error signal. Ascan be appreciated by those skilled in the art of AFM operation, anoperator can observe the output as the cantilever tip tracks the samplesurface, and manually adjust the gain for stable operation accordingly.Alternatively, this gain selection can be automated.

[0134] Next, a multiplier 262 multiplies the scaled error signal by theoutput of driving oscillator 252. The output of multiplier 262 is amodulation of the scaled amplitude error signal at the cantilever drivefrequency. It is subsequently summed with the normal, steady-state drivesignal by summing amplifier 264 to generate a modified cantilever drivesignal.

[0135] The gain applied to the error signal by multiplier 260 as itmodifies the amplitude of the drive oscillator signal determines thedegree to which the cantilever drive is modified in response to thesensed cantilever amplitude, and therefore is indicative of theavailable bandwidth. Note that the ratio of the two summed signals canbe scaled at summing amplifier 264 to scale the amplitude of oscillationof cantilever 20.

[0136] Overall, by actively modifying the cantilever drive signal asdescribed above, active driving circuit 250 ideally optimizes thebandwidth of the response of the cantilever 20, again in the amplitudedomain. As a result, the AFM can maximize scan rate, yet still maintainan acceptable degree of force detection sensitivity. This circuitconfiguration is preferred because of the way the cantilever driveamplitude is controlled in most commercial AFM systems. Differentcantilevers will have different amplitude responses to the same driveamplitude. In a commercial AFM, the drive amplitude to the cantilever isscaled to achieve a predetermined, desirable response amplitude. In thecircuit of the preferred embodiment, this amplitude scaling will alsochange the gain of the drive signal feedback path. As a result, theeffective gain of multiplier gain stage 260 will be the same from onecantilever to the next, once the desired response amplitude has beenachieved.

[0137] A gain and offset topology could also be used as a simplercircuit configuration and an alternate embodiment of amplitude detectioncircuit 259. In such a circuit, the output of multiplier 260 is summedwith an amplitude offset signal at 261 before it is modulated atmultiplier 262. Subsequently, this obviates the need for summingamplifier 264. Although this circuit has the benefit of performing thesumming of the steady state and the dynamic drive amplitude in the lowfrequency domain, where signal processing is generally easier, it is notthe most preferred embodiment because it is not readily compatible withcommercial AFM designs.

[0138] Although the preferred embodiment is described with respect toanalog electronics, the signal could be digitized at any point incircuit 250. The function of any circuit element of circuit 250 could beapproximated by a digital signal processor once the signal has beendigitized. Subsequently, the cantilever drive signal would be convertedback to an analog signal before it is applied to cantilever 20.

[0139] Although the preferred embodiment describes a cantilever 20 withan integrated piezoelectric actuator 36, circuit 250 would also functionwith a conventional, passive cantilever mounted mechanically to apiezo-stack actuator. As mentioned previously, using a passivecantilever will not compromise AFM performance as the active dampingprovided by active driving circuit 250 is applied in the amplitudedomain. For example, any resonance introduced in the mechanical pathbetween the actuator (e.g., piezo-stack) and the cantilever does notaffect the applied damping because the cantilever is not driven by afiltered function of its own deflection, as it is using, for example,circuit 62 shown in FIG. 3. In any event, the advantages of theself-actuated cantilever can be understood by examining FIG. 4, forexample.

[0140]FIG. 12 shows an AFM 270 according to an alternate embodiment thatincorporates the features of AFM 50 (cyclical mode configuration—FIG.2), including two nested feedback loops 272 and 54, with the features ofactive driving circuit 250, including amplitude detection circuit 259(FIG. 11). By dynamically controlling the drive of cantilever 20 withfeedback signals output by circuit 250, the force detection bandwidthrises generally proportionally with a corresponding increase in gain atmultiplier 260. With the control features of AFM 50 (FIG. 2), AFM 270realizes much greater loop bandwidth in cyclical mode, thus achievingmuch greater (and much more commercially viable) throughput per machine.

[0141] In operation, active driving circuit 250 actively modifies theoscillating voltage output of a driving oscillator 252 (and applieddirectly to piezoelectric element 36 of cantilever 20) to optimize thebandwidth of amplitude detection. Active driving circuit 250 utilizes adeflection detector 254 that, as described with respect to FIGS. 1, 2and 11, is preferably an optical detection system including a laser anda photodetector, and which measures cantilever deflection by an opticalbeam bounce technique or another conventional technique. Alternatively,as in the previously described embodiments, deflection detector 254could be (1) a piezoresistor integrated into cantilever 20 with anassociated bridge circuit for measuring the resistance of thepiezoresistor, or (2) a circuit for measuring the impedance of thepiezoelectric element 36 of self-actuated cantilever 20.

[0142] As it senses a deflection of cantilever 18, deflection detector254 transmits a corresponding deflection signal to an RMS-to-DCconverter 256 of active driving circuit 250. The amplitude setpoint isthen subtracted from the RMS amplitude signal by difference amplifier258 to generate an amplitude error signal, as described previously. Theamplitude error signal is then communicated to amplitude detectioncircuit 259 where it is scaled by multiplier gain stage 260. A selectamount of gain for the optimal amount of cantilever dynamic-drivefeedback is applied to the error signal. Typically, a skilled AFMoperator adjusts the gain to achieve optimum performance. The scalederror signal is then fed to second multiplier 262 that multiples thescaled error signal by the output of a driving oscillator 252. Note thatthe output of multiplier 262 is a modulation of the scaled amplitudeerror signal at the cantilever drive frequency. It is subsequentlysummed with the normal, steady-state drive signal output by oscillator252 by summing amplifier 264 to generate a modified cantilever drivesignal.

[0143] Again, the gain applied to the error signal by multiplier 260 asit modifies the amplitude of the drive oscillator signal determines thedegree to which the cantilever drive is modified in response to thesensed cantilever amplitude, and therefore is indicative of theavailable bandwidth. Note that the ratio of the two summed signals canbe scaled at summing amplifier 68 to scale the amplitude of oscillationof cantilever 20.

[0144] When the tip 26 is in close proximity to sample surface 28, theforce interaction between tip 26 and sample surface 28 modifies theamplitude of vibration in cantilever 20. The deflection signal generatedby the deflection detector 254 in response to a detected change in theamplitude of vibration is then converted to an RMS amplitude signal byRMS-to-DC converter 256 to facilitate further processing. Notably, anyknown amplitude detection technique may be used in place of RMS-to-DCconverter 256.

[0145] Similar to AFM 50, the operating RMS amplitude of the cantilevervibration is determined (at least in part) by the setpoint value, whichis subtracted from the cantilever deflection signal by differenceamplifier 258. The error signal generated by difference amplifier 258 isinput to controller 34. Controller 258 applies one or more ofproportional, integral and differential gain to the error signal andcontrols piezoelectric element 36 of self-actuated cantilever 20 to nullthe error signal, thus ensuring that the amplitude of cantileveroscillation is kept generally constant at a value equal to the setpoint.A high voltage amplifier (not shown) may be employed to increase thevoltage of the signal to cantilever 20, but is not required.

[0146] The control signal transmitted by controller 34 to cantilever 20is also input to controller 38 of second feedback loop 54 such thatfirst feedback loop 272 is nested within second feedback loop 54.Preferably, the second setpoint input to controller 38 is a zero valueassociated with AFM actuator 16, in which case the cantilever controlsignal is itself the error signal conditioned by controller 38. Again,PID controller 38 applies one or more of proportional, integral anddifferential gain to the error signal for ultimately controlling Zposition actuator 16 to null the low frequency components of the controlsignal applied to the self-actuated cantilever, when scanning at anoptimum rate. Further, as highlighted above, a high voltage amplifier 40may be employed to increase the voltage of the control signal applied toZ position actuator 16, and is required for most position transducers ofthe scale contemplated by the present invention.

[0147] In sum, AFM 270 combines an AFM Z actuator 16 with aself-actuated cantilever 20 in a manner that allows both high speedimaging and accurate Z position measurement. By actively modifying thecantilever drive signal as described above, active driving circuit 250ideally optimizes the bandwidth of the response of the cantilever 20. Asa result, the AFM can maximize scan rate, yet still maintain anacceptable degree of force detection sensitivity. Further, dependingupon the particular sample topography and the scan rate, the topographycan be mapped by monitoring one of the feedback control signalsindependent of the other.

[0148] Although the best mode contemplated by the inventors of carryingout the present invention is disclosed above, practice of the presentinvention is not limited thereto. It will be manifest that variousadditions, modifications and rearrangements of the features of thepresent invention may be made without deviating from the spirit andscope of the underlying inventive concept.

What is claimed is:
 1. A method of actively changing the bandwidth ofamplitude detection of an AFM having a cantilever, the methodcomprising: applying an oscillating drive signal to the cantilever;measuring a response of the cantilever during operation; demodulatingthe response; and dynamically controlling the oscillating drive signalbased on the demodulated response.
 2. The method according to claim 1,wherein said dynamically controlling step includes using an amplitudedetection circuit.
 3. The method according to claim 2, wherein saiddemodulating step includes using an RMS-to-DC converter to determine anamplitude of the measured response and to generate a correspondingamplitude signal.
 4. The method according to claim 3, further comprisingthe step of generating an error signal based on the amplitude signal,and wherein the amplitude detection circuit includes a gain stage thatapplies a gain to the error signal to generate a modified amplitudesignal.
 5. The method according to claim 4, wherein the gain is manuallyselected by a user.
 6. The method according to claim 4, wherein saiddynamically controlling step includes modulating the oscillating drivesignal with the modified amplitude signal.
 7. The method according toclaim 6, further including the step of summing the modified amplitudesignal with a selected amplitude offset signal.
 8. The method accordingto claim 1, wherein said measuring step includes using an optical beambounce technique.
 9. The method according to claim 1, wherein thecantilever is a self-actuated cantilever.
 10. A method of analyzing asample in cyclical mode with a probe-based AFM, the method comprising:providing a cantilever and a piezo-tube Z position actuator; oscillatingthe cantilever at a predetermined amplitude of oscillation so as tocause a tip of the cantilever to intermittently contact a surface of thesample; scanning the cantilever across the sample; generating adeflection signal in response to said scanning step; generating, with afirst feedback loop, a cantilever control signal in response to thedeflection signal; maintaining the amplitude of oscillation at aconstant value in response to the cantilever control signal; using thecantilever control signal as an error signal in a second feedback loopto control the Z position actuator, wherein the first feedback loop isnested within the second feedback loop; damping the oscillating voltagewith a active drive circuit to actively modify the quality factor (Q) ofthe cantilever resonant frequency during said scanning step; and whereinsaid damping step includes demodulating the deflection signal.
 11. Themethod of claim 10, wherein said demodulating step includes using anamplitude detection circuit.
 12. The method according to claim 11,wherein the amplitude detection circuit includes a gain stage.
 13. Amethod of actively changing the bandwidth of amplitude detection of anAFM, the method comprising: providing a self-actuated cantilever havinga piezoelectric element disposed thereon; providing an active drivingcircuit; driving the self-actuated cantilever with the active drivingcircuit; scanning a surface of a sample with the self-actuatedcantilever; during said scanning step, generating a deflection signal inresponse to a deflection of the self-actuated cantilever; operating theactive driving circuit to actively modify a quality factor (Q)associated with the self-actuated cantilever in response to thedeflection signal; and wherein the active driving circuit demodulatesthe deflection signal and uses the demodulated deflection signal tomodify said driving step.
 14. An AFM for analyzing a surface of asample, the AFM comprising: a cantilever having a tip; an oscillatorthat oscillates said cantilever; and an amplitude detection circuit thatactively modifies the quality factor (Q) associated with the cantileverin the amplitude domain and in response to the deflection signal toactively modify the bandwidth of amplitude detection of the AFM.
 15. AnAFM for analyzing a surface of a sample in cyclical mode, the AFMcomprising: a z-actuator; a cantilever having a tip for scanning thesurface; an active driving circuit that includes an oscillator coupledto the cantilever to oscillate said cantilever; a deflection detectioncircuit that generates a deflection signal in response to deflection ofthe cantilever; and wherein said active drive circuit includes anamplitude detection circuit that actively modifies the quality factor(Q) associated with said cantilever in response to the deflection signalto actively modify the bandwidth of amplitude detection of the AFM inthe amplitude domain.
 16. The method according to claim 15, wherein saidamplitude detection circuit generates an error signal based on saiddeflection signal.
 17. The method according to claim 16, wherein theamplitude detection circuit includes a gain stage that applies a gain tothe error signal to generate a modified deflection signal.
 18. The AFMaccording to claim 17, wherein said oscillator generates an oscillatingdrive signal, and said amplitude detection circuit modulates theoscillating drive signal based on the modified deflection signal.
 19. Amethod of actively changing the bandwidth of amplitude detection of anAFM, the method comprising: providing a self-actuated cantilever havinga piezoelectric element disposed thereon; providing an active drivingcircuit; driving the self-actuated cantilever with the active drivingcircuit; scanning a surface of a sample with the self-actuatedcantilever; during said scanning step, generating a deflection signal inresponse to a deflection of the self-actuated cantilever; operating theactive driving circuit to actively modify a quality factor (Q)associated with the self-actuated cantilever in response to thedeflection signal; and filtering an output of the active driving circuitwith a band-pass filter.